Casual dining sets are used in an everyday setting. They are often used in a breakfast nook or a kitchenette and are usually smaller than a formal table.
Formal dining sets are used in a traditional setting, primarily in a room dedicated for dining. They tend to be large and more elegant.
Counter Height dining sets are usually about 36 inches tall. They are square or circular and there is no "head" of the table. This makes them prefect for use in a social atmosphere such as in a game room.